A posteriori error analysis for a boundary element method with
non-conforming domain decomposition
Catalina Domínguez and Norbert Heuer
Numer. Methods Partial Differential Eq. 30 (3), 947-963, 2014.
We present and analyze an a posteriori error estimator based on mesh refinement
for the solution of the hypersingular boundary integral equation governing the
Laplacian in three dimensions. The discretization under consideration is
a non-conforming domain decomposition method based on the Nitsche technique.
Assuming a saturation property, we establish quasi-reliability and efficiency
of the error estimator in comparison with the error in a natural
(non-conforming) norm.
Numerical experiments with uniform and adaptively refined meshes
confirm our theoretical results.